Solving 3 equations with 3 unknowns

229 次查看（过去 30 天）
Hamza
Hamza 2013-3-5
Dear members;
I would like to solve 3 equations using matlab. following are the 3 equations.
0.0972=ve*ln(mo/(mo-1010mp))
0.11285=ve*ln((mo-1010mp)/(mo-2145mp))
0.10953=ve*ln((mo-2145mp)/(mo-3395mp))
The unknowns in these equations are ve, mo and mp. is there a way to solve for the unknowns?
Thanks in advance

请先登录，再回答此问题。

回答（3 个）

Azzi Abdelmalek
Azzi Abdelmalek 2013-3-5
syms me ve mo mp
eq1=0.0972-ve*log(mo/me)
eq2=0.11285-ve*log((mo-1010*mp)/(mo-2145*mp))
eq3=0.10953-ve*log((mo-2145*mp)/(mo-3395*mp))
solve(eq1,eq2,eq3,ve,mo,mp)
  1 个评论
Hamza
Hamza 2013-3-5
thanks But i guess i don't have the symbolic maths toolbox. can you post me the answers please?
And you can replace 'me' with '(mo-1010mp)' Thanks

请先登录，再进行评论。

Youssef Khmou
Youssef Khmou 2013-3-5
hi try ,
D=solve('x*log(y/a)=0.0972','x*log((y-1010*z)/(y-2145*z))=0.11285','x*log((y-2145*z)/(y-3395*z))=0.10953','x','y','z')
what is me? it is replaced with a
  6 个评论
显示 4更早的评论
Walter Roberson
Walter Roberson 2013-3-6
编辑：Walter Roberson 2013-3-6
One solution is
mo = me, mp = 0, ve = infinity
There might be other solutions; I have my system checking.
... There do not appear to be any other real solutions.
Hamza
Hamza 2013-3-6
these results are based on the new first equation which I have edited?

请先登录，再进行评论。

Roger Stafford
Roger Stafford 2013-3-6
I claim there are either no solutions or infinitely many solutions to your three equations, and I'll tell you why, Hamza. By manipulating the equations appropriately one can rewrite them in the form:
exp(0.0972/ve) = 1/(1-1010*r)
exp(0.11285/ve) = (1-1010*r)/(1-2145*r)
exp(0.10953/ve) = (1-2145*r)/(1-3395*r)
where r = mp/mo. As you can see from this, you have in effect three equations but only two unknowns, namely 've' and 'r', and they are unlikely to have a solution. You can find out if that is so by solving, say, just the first two of these equations. These two can be expressed as:
1-1010*r = exp(-0.0972/ve)
1-2145*r = (1-2145*r)/(1-1010*r) * (1-1010*r)
= exp(-0.11285/ve)*exp(-0.0972/ve)
= exp(-.21005/ve)
Solving for r in each equation gives
r = (1-exp(-0.0972/ve))/1010 = (1-exp(-.21005/ve))/2145
2145*(1-exp(-0.0972/ve)) = 1010*(1-exp(-.21005/ve))
1010*exp(-.21005/ve)-2145*exp(-0.0972/ve)+1135 = 0
You can use matlab's 'fzero' to solve this last equation for 've' and from that determine 'r'. As I say, any such solutions are unlikely to also satisfy the third equation above. If they do, then you will have infinitely many solutions corresponding to all the ways of satisfying r = mp/mo.

类别

在 Help Center 和 File Exchange 中查找有关 Ordinary Differential Equations 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by